Finite Group Databasebeta

← C151×#24990 #50329915

Subgroups — C151×#24990 #50329915

Order 38656.

750 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2538×C151C211yesmaximal, characteristic
2Q8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
3#2099×C151C212yesmaximal, complemented
4#2071×C151C212yesmaximal
5#1984×C151C211yesmaximal, characteristic, complemented
6#1947×C151C211yesmaximal, characteristic, complemented
7#1925×C151C212yesmaximal
8#1918×C151C212yesmaximal, complemented
9#1834×C151C211yesmaximal, characteristic, complemented
10#1802×C151C211yesmaximal, characteristic
11C4×#102×C151C211yesmaximal, characteristic
12C2×C22⋊Q8×C151—21no—
13C2×C4×Q8×C151—21no—
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16C2×#107×C151C2212yes—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×#102×C151C2211yescharacteristic
19C2×#102×C151C2212yes—
20C2×#102×C151C2211yescharacteristic
21C2×C4×C8×C151C2211yescharacteristic
22#396×C151—22no—
23#390×C151C2212yes—
24#389×C151—21no—
25#389×C151—22no—
26#389×C151C2212yes—
27#384×C151C2211yescharacteristic
28#384×C151C2211yescharacteristic
29#384×C151C2212yes—
30#380×C151—21no—
31C4×C4⋊C4×C151C2212yes—
32C4×C4⋊C4×C151C2211yescharacteristic
33#340×C151C2212yes—
34#340×C151C2212yes—
35#340×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#340×C151C2211yescharacteristic
39#336×C151C2212yes—
40#336×C151C2212yes—
41C22×Q8×C151D411yescharacteristic
42C22×D4×C151C2311yescharacteristic
43C23×C4×C151—21no—
44C22×C8×C151C2311yescharacteristic
45C22×C8×C151C2311yescharacteristic
46C22×C8×C151C2312yes—
47C22⋊Q8×C151—44no—
48C4×Q8×C151—22no—
49C4×Q8×C151—22no—
50C4×Q8×C151—44no—
51C4×D4×C151—22no—
52C4×D4×C151—22no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151D411yescharacteristic
61C2×C4⋊C4×C151D412yes—
62C2×C4⋊C4×C151C2311yescharacteristic
63C2×C4⋊C4×C151C2312yes—
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—22no—
70C2×C42×C151—22no—
71C2×C42×C151—21no—
72C2×C42×C151C2312yes—
73C2×C42×C151C2311yescharacteristic
74#107×C151—24no—
75C4⋊C8×C151—22no—
76#102×C151—24no—
77#102×C151—22no—
78#102×C151—22no—
79C4×C8×C151—22no—
80#95×C151—22no—
81#95×C151—21no—
82#95×C151—22no—
83C24×C151—21no—
84C2×Q8×C151—22no—
85C2×Q8×C151—22no—
86C2×Q8×C151D814yes—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151#4112yes—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—22no—
96C22×C4×C151—21no—
97C22×C4×C151—22no—
98C22×C4×C151—42no—
99C22×C4×C151—42no—
100C22×C4×C151—42no—
101C22×C4×C151C2×D412yes—
102C22×C4×C151C2×D411yescharacteristic
103C22×C4×C151C2×D412yes—
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2411yescharacteristic
106C2×C8×C151—21no—
107C2×C8×C151—21no—
108C2×C8×C151—22no—
109C2×C8×C151—21no—
110C2×C8×C151—21no—
111C2×C8×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151—21no—
114C2×C8×C151—21no—
115C4⋊C4×C151—24no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—21no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—21no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—44no—
127C4⋊C4×C151—42no—
128C4⋊C4×C151—42no—
129C4⋊C4×C151—44no—
130C4⋊C4×C151—81no—
131C4⋊C4×C151—81no—
132C4⋊C4×C151—82no—
133C4⋊C4×C151#4112yes—
134C22⋊C4×C151—42no—
135C22⋊C4×C151—44no—
136C22⋊C4×C151—82no—
137C42×C151—22no—
138C42×C151—22no—
139C42×C151—44no—
140C42×C151—42no—
141C42×C151#4112yes—
142C42×C151#4112yes—
143C23×C151—22no—
144C23×C151—41no—
145C23×C151—41no—
146C23×C151—41no—
147C23×C151—41no—
148C23×C151—41no—
149C23×C151—41no—
150C23×C151C22×D411yescharacteristic
151Q8×C151—28no—
152D4×C151—22no—
153D4×C151—22no—
154D4×C151—41no—
155D4×C151—41no—
156C2×C4×C151—22no—
157C2×C4×C151—22no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—41no—
170C2×C4×C151—42no—
171C2×C4×C151—41no—
172C2×C4×C151—42no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—42no—
176C2×C4×C151—42no—
177C2×C4×C151—41no—
178C2×C4×C151—84no—
179C2×C4×C151#12312yes—
180C2×C4×C151#12312yes—
181C2×C4×C151C2×D814yes—
182C2×C4×C151C2×D812yes—
183C2×C4×C151#13712yes—
184C2×C4×C151C2×#4111yescharacteristic
185C2×C4×C151C2×#4111yescharacteristic
186C2×C4×C151C2×#4111yescharacteristic
187C2×C4×C151C2×#4111yescharacteristic
188C2×C4×C1512−1+411yescharacteristic
189C2×C4×C1512−1+411yescharacteristic
190C8×C151—42no—
191C8×C151—41no—
192C8×C151—41no—
193C22×C151—42no—
194C22×C151—42no—
195C22×C151—42no—
196C22×C151—81no—
197C22×C151—81no—
198C22×C151—81no—
199C22×C151—81no—
200C22×C151C2×#12311yescharacteristic
201C22×C151#54811yescharacteristic
202C22×C151#54811yescharacteristic
203C22×C151C22×D811yescharacteristic
204C22×C151C2×#13711yescharacteristic
205C22×C151#57711yescharacteristic
206C22×C151#57711yescharacteristic
207C4×C151—24no—
208C4×C151—22no—
209C4×C151—42no—
210C4×C151—42no—
211C4×C151—81no—
212C4×C151—82no—
213C4×C151—82no—
214C4×C151—81no—
215C4×C151#48014yes—
216C4×C151#52911yescharacteristic
217C4×C151#54111yescharacteristic
218C4×C151#55211yescharacteristic
219C4×C151#55611yescharacteristic
220C2×C151—82no—
221C2×C151#242111yescharacteristic
222C2×C151C2×#48011yescharacteristic
223C2×C151#309911yescharacteristic
224C2×C151#335811yescharacteristic
225C2×C151#335811yescharacteristic
226C2×C151#336911yescharacteristic
227C2×C151#337211yescharacteristic
228#24990C15111yesmaximal, characteristic, direct product factor, Sylow
229C151#2499011yescharacteristic, direct product factor, Sylow
230#2538C2×C15111yescharacteristic
231Q8×C4⋊C4C2×C15111yescharacteristic, complemented
232#2099C2×C15112yescomplemented
233#2071C2×C15112yes—
234#1984C2×C15111yescharacteristic, complemented
235#1947C2×C15111yescharacteristic, complemented
236#1925C2×C15112yes—
237#1918C2×C15112yescomplemented
238#1834C2×C15111yescharacteristic, complemented
239#1802C2×C15111yescharacteristic
240C4×#102C2×C15111yescharacteristic
241C2×C22⋊Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C22×C15111yescharacteristic
244C2×C4×D4C22×C15111yescharacteristic
245C2×#107C22×C15112yes—
246C2×C4⋊C8C22×C15111yescharacteristic
247C2×#102C22×C15112yes—
248C2×#102C22×C15111yescharacteristic
249C2×#102C22×C15111yescharacteristic
250C2×C4×C8C22×C15111yescharacteristic
251#396—22no—
252#390C22×C15112yes—
253#389—21no—
254#389—22no—
255#389C22×C15112yes—
256#384C22×C15111yescharacteristic
257#384C22×C15112yes—
258#384C22×C15111yescharacteristic
259#380—21no—
260C4×C4⋊C4C22×C15112yes—
261C4×C4⋊C4C22×C15111yescharacteristic
262#340C22×C15112yes—
263#340C22×C15112yes—
264#340C22×C15112yes—
265#340C22×C15112yes—
266#340C22×C15111yescharacteristic
267#340C22×C15111yescharacteristic
268#336C22×C15112yes—
269#336C22×C15112yes—
270C22×Q8D4×C15111yescharacteristic
271C22×D4C23×C15111yescharacteristic
272C23×C4—21no—
273C22×C8C23×C15111yescharacteristic
274C22×C8C23×C15111yescharacteristic
275C22×C8C23×C15112yes—
276C22⋊Q8—44no—
277C4×Q8—22no—
278C4×Q8—22no—
279C4×Q8—44no—
280C4×D4—22no—
281C4×D4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4D4×C15111yescharacteristic
290C2×C4⋊C4D4×C15112yes—
291C2×C4⋊C4C23×C15111yescharacteristic
292C2×C4⋊C4C23×C15112yes—
293C2×C4⋊C4C23×C15111yescharacteristic
294C2×C4⋊C4C23×C15112yes—
295C2×C4⋊C4C23×C15111yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C42—22no—
300C2×C42—21no—
301C2×C42C23×C15112yes—
302C2×C42C23×C15111yescharacteristic
303#107—24no—
304C4⋊C8—22no—
305#102—24no—
306#102—22no—
307#102—22no—
308C4×C8—22no—
309#95—22no—
310#95—21no—
311#95—22no—
312C24—21no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8D8×C15114yes—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4#41×C15112yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4C2×D4×C15112yes—
331C22×C4C2×D4×C15111yescharacteristic
332C22×C4C2×D4×C15112yes—
333C22×C4C2×D4×C15111yescharacteristic
334C22×C4C24×C15111yescharacteristic
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—21no—
343C2×C8—21no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—44no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—44no—
359C4⋊C4—81no—
360C4⋊C4—81no—
361C4⋊C4—82no—
362C4⋊C4#41×C15112yes—
363C22⋊C4—42no—
364C22⋊C4—44no—
365C22⋊C4—82no—
366C42—22no—
367C42—22no—
368C42—44no—
369C42—42no—
370C42#41×C15112yes—
371C42#41×C15112yes—
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C22×D4×C15111yescharacteristic
380Q8—28no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—84no—
408C2×C4#123×C15112yes—
409C2×C4#123×C15112yes—
410C2×C4C2×D8×C15114yes—
411C2×C4C2×D8×C15112yes—
412C2×C4#137×C15112yes—
413C2×C4C2×#41×C15111yescharacteristic
414C2×C4C2×#41×C15111yescharacteristic
415C2×C4C2×#41×C15111yescharacteristic
416C2×C4C2×#41×C15111yescharacteristic
417C2×C42−1+4×C15111yescharacteristic
418C2×C42−1+4×C15111yescharacteristic
419C8—42no—
420C8—41no—
421C8—41no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C2×#123×C15111yescharacteristic
430C22#548×C15111yescharacteristic
431C22#548×C15111yescharacteristic
432C22C22×D8×C15111yescharacteristic
433C22C2×#137×C15111yescharacteristic
434C22#577×C15111yescharacteristic
435C22#577×C15111yescharacteristic
436C4—24no—
437C4—22no—
438C4—42no—
439C4—42no—
440C4—82no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4#480×C15114yes—
445C4#529×C15111yescharacteristic
446C4#541×C15111yescharacteristic
447C4#552×C15111yescharacteristic
448C4#556×C15111yescharacteristic
449C2—82no—
450C2#2421×C15111yescharacteristic
451C2C2×#480×C15111yescharacteristic
452C2#3099×C15111yescharacteristic
453C2#3358×C15111yescharacteristic
454C2#3358×C15111yescharacteristic
455C2#3369×C15111yescharacteristic
456C2#3372×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. Q8×C4⋊C4×C151C2semidirect
3. #2099×C151C2semidirect
5. #1984×C151C2semidirect
6. #1947×C151C2semidirect
8. #1918×C151C2semidirect
9. #1834×C151C2semidirect
228. #24990C151direct (N × H)
229. C151#24990direct (N × H)
231. Q8×C4⋊C4C2×C151semidirect
232. #2099C2×C151semidirect
234. #1984C2×C151semidirect
235. #1947C2×C151semidirect
237. #1918C2×C151semidirect
238. #1834C2×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#2538×C1512
Q8×C4⋊C4×C1512
#2099×C1512
#2071×C1512
#1984×C1512
#1947×C1512
#1925×C1512
#1918×C1512
#1834×C1512
#1802×C1512
C4×#102×C1512
#24990151